either make y a function of x, which is trival but dull or just differentiate everything wrt x and use the chain rule and product rule.

example, one you can do anyway, suppose xy=1

then assuming this implicitly defines a function y in terms of x (notice that word implicit, look in your notes for a reference to it)

then [tex]\frac{d}{dx}xy = \frac{d}{dx}1[/tex] that is to say [tex] (\frac{d}{dx}x)y + x(\frac{d}{dx}y) = 0[/tex]. of course dx/dx=1 so, [tex]y+ x\frac{dy}{dx}=0[/tex] and we see that [tex]\frac{dy}{dx} = -y/x[/tex] recall that y= 1/x, and we see [tex]\frac{dy}{dx} = -1/x^2[/tex] try and apply this idea to you example

I'm a little confused with the answers above. When differentiating some function of y with respect to x, is it not simply the derivate of the function with respect to y multiplies by the derivative of y with respect to x?

Originally posted by Zurtex I'm a little confused with the answers above. When differentiating some function of y with respect to x, is it not simply the derivate of the function with respect to y multiplies by the derivative of y with respect to x?

I gave that example for two reasons: it was easy to rearrange and solve without implicit differentiation, so that you could see that you got the answer you thought you ought to get, and because I didn't want to just solve your homework problem for you, but to prompt you into trying it again for yourself, changind the details as necessary.